How do you identify the important parts of #y= 6x^2 +2x+4# to graph it?

Question

Eva Adamson · Accepted Answer

Graph #y = 6x^2 + 2x + 4# The important parts to graph y are: a. x-coordinate of vertex and axis of symmetry: #x = (-b/2a) = -2/12 = -1/6# y-coordinate of vertex: #y = f(-1/6) = 1/6 - 2/6 + 4 = 23/6.# b. y-intercept. Make x = 0 --> y = 4 x-intercepts. Make y = 0 and solve #6x^2 + 2x + 4 = 0.# Since D = 4 - 96 < 0, there are no x-intercepts (no real roots). The parabola is completely above the x-axis and it opens upward (a > 0). graph{6x^2 + 2x + 4 [-40, 40, -20, 20]}

Jameson Allen · Answer

undefined To graph the function y = 6x^2 + 2x + 4, you can identify the important parts by analyzing its components:

1. The coefficient of x^2 (6): Indicates the shape of the parabola. A positive coefficient means the parabola opens upwards, and a negative coefficient means it opens downwards.
2. The coefficient of x (2): Determines the slope of the line tangent to the curve at any given point. It also affects the location of the vertex.
3. The constant term (4): Represents the y-intercept, which is the point where the parabola intersects the y-axis.

By understanding these components, you can sketch the graph of the quadratic function.